I'm pretty sure you could legitimately have a group for:
a] Same-sex attracted women, including those attracted to both sexes;
b] Women who are exclusively attracted to women;
c] Only women who are attracted to both sexes;
d] Same-sex attracted men, including bisexual men;
e] Exclusively gay men;
f] Only bisexual men;
g] LGB of both sexes;
h] Exclusively same-sex attracted men and women;
i] Exclusively bisexual men and women;
j] Transbians and TW-attracted women, though you couldn't justify this on sex grounds and would have to be prepared for others to apply;
k] Transgay and TM-attracted men, same caveat;
l] All LGBT.
Not terribly restrictive, is it?
(edited to invent 'transgay' although I bet it's already a term)